E-10: Let f(x) be a non-constant polynomial satisfying the relation f(x).f (y) = f (x)+ f (y)+f(xy)-2, for all real x', 'y'and f (0)#1, suppose f(4) = 65, then a) f'(x) is a polynomial of degree 2 b) roots of f'(x)= 2x+1 are real %3D c) x.f'(x) = 3(f(x)-1) d) f'(-1)= 3

Q: u(0,1)= 0, U(1,1)=0, u(x,0)=2x u(x,0)=2 ALE. A Q.4/Answer ONLY TWO, Except (C) (4) Using Lagrange…

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Q: e*+1 Differentiate the function f(x)= In -3x +1 -3e A) 4e** +1 +1 3e B) e +1 +1 3e C) 3x 1. D) E) +1

A: Topic: differentiation

Q: Let f and g be functions defined by, f(x) = Vx+ 2 and g(x) = Vx2 + 1. Find the functions gof, , f +…

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Q: The graph of function f(x) = x³ 6x2 + 9x + 1 is concave upward on (-∞, 2) (-0, 0) (2, оо) о (-2, 2)

A: f is concave up when f''(x) is greater than 0

Q: The domain of the function f(x)=√12+4x−x^2 is the closed interval [A,B] where A= and B=

A: Domain is the set of all values that can be taken by x so that the equation is defined.

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: Let f(x) = e^x. Find the polynomial P2(x) of degree at most 2 such that P2(1) = f(1), P2(2) = f(2),…

A: We have to find the polynomial of degree 2 for the function fx=ex using the divided difference…

Q: = a are given. Evaluate f(z) dr. on (b-a) +2 (ab - a) - 2 a+b) +2 a-b) - 2 II la + b) - 2

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Q: Verify that f′(x) = g′(x) and explain the relationship between f and g

A: fx=3xx+2f'x=ddx3xx+2=x+2(3)-(3x)(1)x+22=3x+6-3xx+22=6x+22

Q: What is the point of intersection for f(x) = 2* and g (x) = (÷) ? A (1,0) (2,4) C (1.) (0.1)

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Q: 1 x-2 f(x)=- y g(x)=√x

A: To find the composite function

Q: x3 +x2 3 Prove that if f (x) then f"(x) = – x² Find g'(x) and g"(x) if g(x) = (2x – 3)² (x + 4)³. 2…

A: Ans (1). Given that, f(x) = x3+x2-12x2 f(x) = x + 1 - 12x2 now differentiate the function, f'(x) = 1…

Q: Discuss the analyticity of  f(z) = Re(z 3)   Find whether the given function is analytic or not.…

A: A complex valued complex variable function is analytics at z0 if it is differentiable every point in…

Q: Let f(x) = x3 + 5. Explain why f(x) is invertible, then show all steps in the derivation of a…

A: Invertible function and it's inverse.

Q: For any function, With utilization of the product rule for functions of one variable (eq1), show /…

A: Consider the function z=f(x)·g(x) where f and g are both function of x. So we can rewrite the…

Q: Differentiate the functions. a) f(x) = 2 – 5x + b) f(x) = e* + sinx c) f(x) =

A: Differentiate wrt x

Q: Derive a 2nd order accurate finite difference expression for the first derivative at point i-1,…

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Q: The function, r= 3t°, y =ť –t is concave upward on the interval (a) (-∞,0) (b) (0, 0) (c) (-0,0) (d)…

A: The general form of the parametric equation of the curve in two-dimensional space is given by…

Q: Find all poles, their order and their residues for the function f(z)=(z+1/z-1)3  ( z+1 in numerator…

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Q: The inverse of function f(x) = x3 + 2 is а) f-1 (y) %3 (у - 2) 1/2 b) f-1 (y) = (y – 2) 1/3 c) f-1…

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Q: Express the function in the form fog. (i) F(x) = (2r + r*)ª. (ii) F(r) = %3D 1+ VE

A: Answer